Ken Livingstone has guest edited this week's issue of the New Statesman magazine – signalling an end to his estrangement from the left-of-centre weekly.

The former London mayor has penned the magazine's leader column, calling for Labour to change, and interviewed one of his favourite authors, Iain M Banks.

This week's magazine also features a piece by the singer Jarvis Cocker advocating the scrapping of Trident. Other contributors include Vivienne Westwood, Stephen Fry, Bonnie Greer, Jo Brand, Charlotte Raven and Norman Cook.

Livingstone's decision to guest-edit the News Statesman suggests a thawing of relations with the title. Last year the magazine's then political editor, Martin Bright, presented a Channel 4 Dispatches documentary critical of his time as mayor and wrote in the London Evening Standard: "I now believe Ken Livingstone is a disgrace to his office and not fit to be Mayor of London."

Bright and John Kampfner, New Stateman editor at the time of the Dispatches documentary, have since left the magazine, as has its then owner, the Labour MP Geoffrey Robinson, who was said to have been against the attack on Livingstone.

Jason Cowley, who took over as New Stateman editor in September last year, approached Livingstone two months ago with the idea.

"New Statesman editor Jason Cowley has kindly relinquished the reins of the magazine and passed them over to me and I hope I've done him and his team proud," Livingstone said.

"A magazine like the Statesman is more essential than ever when we face the challenge of global economic crisis and the threat of climate change, and when only progressive politics can provide the answers – or even ask the right questions. My one-off edition will try to get as many of the world's biggest issues together in one place. It will not flinch from saying why the Tories will be a disaster to why Labour must change. From Obama and US cities to whether or not you need socialism to survive in outer space, it's all here."